How to make a shortcut for this button?
Press Ctrl+Alt+U to bring up User Preferences. Then go to the Input tab. Then expand Image, there you'll find UV Editor. Expand that and scroll down to the bottom and click on + Add New button.

In the identifier, input this: wm.context_toggle. Then in the context attribute, input tool_settings.use_uv_select_sync.

Finally select an unused keyboard shortcut. I used ` in this case. Select to Save User Settings so you don't have to do this every time you start Blender.